A non-steady-state slurry diffusion process simulation method and system considering slurry-rock coupling effect

Abstract

The application discloses a kind of non-steady-state slurry diffusion process simulation method and system considering slurry-rock coupling effect, belong to rock mass engineering grouting technical field, comprising: step 1, define the basic assumption of slurry and fissure;Step 2, based on the basic assumption of slurry and fissure, establish slurry flow control equation and fissure deformation control equation;Step 3, based on slurry flow control equation and fissure deformation control equation, establish non-steady-state slurry-rock coupling pressure control equation;Step 4, based on the basic assumption of slurry and fissure, establish initial condition, boundary condition and grouting body condition, combined with non-steady-state slurry-rock coupling pressure control equation, build non-steady-state slurry diffusion model considering slurry-rock coupling effect;Step 5, numerical solution is carried out to non-steady-state slurry diffusion model using finite volume method.The application is suitable for grouting design and optimization in the fields of tunnel engineering, mine engineering, geological disaster prevention and the like, and can provide theoretical support and technical guidance for engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of rock mass engineering grouting technology, specifically relating to a method and system for simulating unsteady grout diffusion processes that considers the grout-rock coupling effect. Background Technology

[0002] Grouting is an important reinforcement and seepage prevention method in rock engineering, widely used in tunnel engineering, mining engineering, and geological disaster prevention. Grouting involves injecting grout into rock fissures, filling them and forming a solidified mass, thereby improving the strength and stability of the rock mass and preventing groundwater leakage. However, the diffusion behavior of the grout in fissures during grouting is influenced by various factors, including the rheological properties of the grout, the geometry of the fissures, the mechanical properties of the rock mass, the instability of the grouting pressure, and the force coupling effect between the grout and the rock mass. Traditional grouting models are often based on simplified assumptions and cannot accurately describe the diffusion behavior of the grout in fissures. In grouting theory research, the rheological properties of the grout are a key factor. Traditional models typically assume the grout is a Newtonian fluid, neglecting the yield stress and the time-varying characteristics of yield stress and viscosity. However, cement-water glass quick-setting grouts commonly used in practical engineering exhibit significant non-Newtonian fluid characteristics, with their yield stress and viscosity changing significantly over time. This characteristic makes the diffusion behavior of grout in fractures more complex, and traditional Newtonian fluid models struggle to accurately describe it. Furthermore, the geometry of the fractures and the mechanical properties of the rock mass also significantly influence grout diffusion. Traditional grouting models typically assume a constant fracture aperture, neglecting the effect of grout pressure on it. However, in actual grouting processes, grout pressure causes changes in fracture aperture, thus affecting the grout diffusion range and pressure distribution. This coupling effect between the grout and the rock mass is often ignored in traditional models, leading to significant discrepancies between simulation results and actual engineering conditions.

[0003] In recent years, with the continuous development of grouting technology, the non-Newtonian fluid properties of grout, the elastic deformation of fractures, and the grout-rock coupling effect have gradually become research hotspots. Some scholars have proposed grouting models that consider the time-varying characteristics of grout yield stress and viscosity, but these models are mostly based on steady-state assumptions and ignore the unsteady-state effects of grout pressure changing with time.

[0004] Therefore, it is necessary to design a simulation method and system for the unsteady slurry diffusion process that considers the slurry-rock coupling effect to address the above problems. Summary of the Invention

[0005] The purpose of this invention is to address the problem that models based on steady-state assumptions neglect the unsteady effects of grout pressure changes over time. It provides a method and system for simulating the unsteady grout diffusion process that considers the grout-rock coupling effect. Based on fracture flow theory, and combining grout flow, fracture deformation, and unsteady effects, a grout diffusion model in fractured rock mass is constructed. The model is then numerically solved using the finite volume method (FVM), which can accurately simulate the grout diffusion process in fractures, predict grout pressure distribution, fracture aperture changes, and capture the grout diffusion range at all times.

[0006] According to one aspect of this specification, a method for simulating unsteady slurry diffusion processes considering slurry-rock coupling effects is provided, comprising:

[0007] Based on fracture flow theory, the basic assumptions for slurry and fractures are defined;

[0008] Based on the fundamental assumptions about slurry and cracks, slurry flow control equations and crack deformation control equations are established.

[0009] Based on the slurry flow control equation and the fracture deformation control equation, an unsteady slurry-rock coupled pressure control equation is established.

[0010] Based on the basic assumptions of grout and fractures, initial conditions, boundary conditions and grouting body conditions are established. Combined with the unsteady grout-rock coupling pressure control equation, an unsteady grout diffusion model considering the grout-rock coupling effect is built.

[0011] The finite volume method is used to numerically solve the unsteady slurry diffusion model, realizing the simulation of the unsteady slurry diffusion process considering the slurry-rock coupling effect.

[0012] Furthermore, the basic assumptions for defining grout and fractures include:

[0013] (1) Assume that the slurry is an incompressible, homogeneous, and isotropic Bingham fluid;

[0014] (2) Assume that the flow velocity of the grout on the upper and lower sidewalls of the crack is 0;

[0015] (3) Assume that the grout only diffuses in the cracks;

[0016] (4) Assume that the cracks are horizontally distributed;

[0017] (5) Assume that the slurry flows in laminar flow within the fracture.

[0018] (6) Assume that the rock mass on both sides of the fracture undergoes only elastic deformation;

[0019] (7) Assume that the pressure at the slurry diffusion front is always equal to the static pressure.

[0020] Furthermore, the governing equations for slurry flow and crack deformation are established, including:

[0021] The equation governing the slurry flow is expressed as follows:

[0022]

[0023] in, This represents the average flow of slurry diffusing along the fracture direction, where b represents the fracture aperture. Represents the time-varying function of slurry viscosity. This represents the real variation function of the slurry yield stress. Indicates the slurry pressure gradient. This represents the critical pressure gradient at which Bingham fluid begins to flow;

[0024] The expression for the crack deformation control equation is:

[0025]

[0026] Where b0 is the initial crack aperture, P is the grout pressure, and P s K is the threshold pressure for crack deformation. n Let K be the normal elastic coefficient, where K is the normal elastic coefficient. n =D / E, where D is the grouting influence range and E is the rock mass elastic modulus.

[0027] Furthermore, the unsteady magma-rock coupled pressure governing equations are established, including:

[0028]

[0029] in, The distance between any point within the fissure and the grouting port. This represents the rate of change of grout pressure at any location within the fracture over time. The rate of change along the direction of slurry radiative diffusion. This represents the grout flow rate at any location within the fracture, where Indicates the crack aperture. This indicates the slurry flow rate.

[0030] Furthermore, initial conditions, boundary conditions, and grouting volume conservation conditions are established, including:

[0031] At the initial moment, the pressure at each location in the fracture is the fracture hydrostatic pressure.

[0032] At the grouting port, the grouting pressure is set as a boundary condition, and at the grout diffusion front, the fracture hydrostatic pressure is set as a boundary condition.

[0033] During the process of grout displacing the fracture medium, the volume of grout injected through the injection port and the volume of grout retained in the fracture are kept constant.

[0034] Furthermore, the finite volume method is used to numerically solve the unsteady slurry diffusion model, including:

[0035] The computational domain of the unsteady slurry diffusion model is meshed and spatially discretized using polar coordinates.

[0036] The slurry flow control equation and the unsteady slurry-rock coupled pressure control equation are discretized, and discrete equations are constructed.

[0037] Discretize the grout volume conservation condition to obtain a real-time characterization of the grout diffusion front radius;

[0038] Spatial mapping and capture of the slurry reaction time at grid nodes within the slurry range;

[0039] The pressure and crack aperture distributions are iteratively corrected until the convergence condition is met, and finally the slurry pressure distribution, crack aperture change and slurry diffusion range are obtained.

[0040] According to one aspect of this specification, a simulation system for unsteady slurry diffusion processes considering slurry-rock coupling effects is provided, comprising:

[0041] The basic assumption setting module is used to define the basic assumptions about slurry and fractures based on fracture flow theory;

[0042] The governing equation establishment module is used to establish the slurry flow control equation and the crack deformation control equation based on the basic assumptions of slurry and cracks.

[0043] The coupled control equation establishment module is used to establish unsteady magma-rock coupled pressure control equations based on slurry flow control equations and fracture deformation control equations.

[0044] The diffusion model building module is used to establish initial conditions, boundary conditions and grouting body conditions based on the basic assumptions of grout and fractures. Combined with the unsteady grout-rock coupling pressure control equation, it builds an unsteady grout diffusion model that considers the grout-rock coupling effect.

[0045] The model solver module is used to numerically solve the unsteady slurry diffusion model using the finite volume method, thereby simulating the unsteady slurry diffusion process that takes into account the slurry-rock coupling effect.

[0046] According to one aspect of this specification, an electronic device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the simulation method for unsteady slurry diffusion processes considering slurry-rock coupling effects.

[0047] According to one aspect of this specification, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for simulating unsteady slurry diffusion processes considering slurry-rock coupling effects.

[0048] Compared with the prior art, the beneficial effects of the present invention are:

[0049] 1. By defining the basic assumptions of grout and fractures and establishing the unsteady grout-rock coupled pressure control equation, this invention can more comprehensively consider the changes in grout pressure over time and the dynamic adjustment of fracture opening, thereby more accurately describing the unsteady effect of grout diffusion.

[0050] 2. This invention establishes an unsteady grout diffusion model that considers the grout-rock coupling effect, which can accurately simulate the diffusion process of grout in fractures. The finite volume method is used to numerically solve the unsteady grout diffusion model, predicting the grout pressure distribution, fracture aperture changes, and capturing the grout diffusion range at all times. This can efficiently and accurately simulate the diffusion process of grout in fractures, significantly improving computational efficiency. In addition, this invention can provide theoretical support and technical guidance for engineering practice, optimize grouting parameters, improve grouting effect and engineering safety, reduce engineering costs, and significantly improve the scientificity and reliability of engineering design. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart illustrating the overall method calculation process according to an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram illustrating the force analysis of slurry flow in a crack in an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the crack opening driven by grouting pressure and a curve of crack opening as a function of grout pressure in an embodiment of the present invention.

[0055] Figure 4 This is a schematic diagram of crack opening and closing under unstable grouting pressure in an embodiment of the present invention;

[0056] Figure 5 This is a schematic diagram of the control volume establishment and mesh generation in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram of the time-space mapping strategy for the degree of slurry reaction in an embodiment of the present invention;

[0058] Figure 7 These are time-varying curves of the slurry diffusion front radius and the slurry flow velocity at the injection port under different working conditions in this embodiment of the invention.

[0059] Figure 8 This is a schematic diagram showing the distribution of grout pressure and crack opening along the grouting path under different working conditions at a grouting time of 10s in an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] like Figure 1 As shown, this embodiment of the invention provides a method for simulating unsteady slurry diffusion processes considering the slurry-rock coupling effect, including: Step 1, defining basic assumptions about slurry and fractures based on fracture flow theory. Step 2, establishing slurry flow control equations and fracture deformation control equations based on the basic assumptions about slurry and fractures, and then establishing unsteady slurry-rock coupling pressure control equations. Step 3, establishing initial conditions, boundary conditions, and grouting body conditions based on the basic assumptions about slurry and fractures, and constructing an unsteady slurry diffusion model considering the slurry-rock coupling effect by combining the unsteady slurry-rock coupling pressure control equations. Step 4, numerically solving the unsteady slurry diffusion model using the finite volume method to simulate the unsteady slurry diffusion process considering the slurry-rock coupling effect.

[0062] Specifically, the embodiments of the present invention also provide the following details for step 1: 1. Assume the grout is an incompressible, homogeneous, and isotropic Bingham fluid. 2. Assume the upper and lower sidewalls of the fracture satisfy the no-slip boundary condition, i.e., the flow velocity of the grout on the upper and lower sidewalls of the fracture is 0. 3. Ignore the grout loss caused by grout infiltration into the rock mass on both sides of the fracture, and assume the grout only diffuses within the fracture. 4. Assume the fracture is horizontally distributed with a uniform initial fracture aperture, and disregard the influence of gravity on the grout diffusion process, assuming the grout's movement mode within the fracture is laminar flow. 5. Assume the rock mass on both sides of the fracture undergoes only elastic deformation. 6. During the grout diffusion process, the flow of the grout dispersing medium is not considered, i.e., the pressure at the grout diffusion front is always equal to the static pressure.

[0063] Specifically, the embodiments of the present invention also provide the specific content of step 2: as follows Figure 2-3As shown, the slurry flow control equation and the crack deformation control equation are introduced respectively, as follows: Figure 4 As shown, an unsteady grout-rock coupled pressure control equation is established. The time-varying characteristics of grout yield stress and viscosity, as well as the influence of grout pressure on fracture aperture, are considered. Furthermore, the dynamic adjustment of fracture aperture due to the unsteady characteristics of grout pressure changing over time is also taken into account, as detailed below:

[0064] Step 2.1: Establish the governing equations for slurry flow:

[0065] (1)

[0066] in, b represents the average velocity of the slurry spreading along the crack direction; b represents the crack aperture. This represents a time-varying function of slurry viscosity; This represents the real variation function of the slurry yield stress; Indicates the slurry pressure gradient; This represents the critical pressure gradient at which Bingham fluid flows, an effect primarily controlled by the slurry's yield stress. When the friction pressure gradient at a point in the fracture is less than this critical pressure gradient, the slurry is considered not to be flowing.

[0067] Step 2.2: Establish the governing equations for crack deformation:

[0068] (2)

[0069] Where b0 is the initial crack aperture; P is the grout pressure; P s K is the threshold pressure for crack deformation. n =D / E, representing the normal elastic coefficient, where D is the grouting influence range and E is the rock mass elastic modulus.

[0070] Step 2.3: Establish the unsteady magma-rock coupled pressure control equations:

[0071] (3)

[0072] in, The distance between any point within the fissure and the grouting port. This represents the rate of change of grout pressure at any location within the fracture over time. This represents the rate of change (gradient) along the direction of slurry radiation diffusion. This represents the grout flow rate at any location within the fracture, where Indicates the crack aperture. This indicates the slurry flow rate.

[0073] Specifically, the embodiments of the present invention also provide the specific content of step 3:

[0074] Step 3.1: Establish initial conditions, boundary conditions, and grouting volume conservation conditions:

[0075] 1. Initially, the fracture is filled with water, and the pressure at each location is the fracture hydrostatic pressure. :

[0076] (4)

[0077] Where r represents the position (with the grouting port as the origin of the coordinate system), t represents the grouting time, and formula (4) means that at the initial time t=0.

[0078] 2. At the grouting port At the injection point, pressure-controlled grouting is used, meaning the grouting pressure is set as the boundary condition at the injection port, and the injection pressure is adjusted accordingly. It is known that its value can change with time, but remains consistent with the fracture hydrostatic pressure at the initial moment:

[0079] (5)

[0080] in, The radius of the grouting inlet. Indicates grouting time, This indicates the injection pressure at the grouting port when the grouting time t=0.

[0081] 3. At the slurry diffusion front (i.e., the slurry-water interface), the influence of water flow is not considered, meaning that the location is always under the hydrostatic pressure of the fracture. :

[0082] (6)

[0083] in, This indicates the radius of the slurry diffusion front.

[0084] 4. During the process of grout displacing the fractured medium, the grout diffusion range within the fracture changes over time. It is necessary to maintain the conservation of the amount of grout injected through the grouting port and the amount of grout retained within the fracture from the start of grouting to a certain point in time.

[0085] (7)

[0086] in, This represents the change in grouting volume with grouting time t. To open the crack at the grouting port location, This refers to the grout flow rate at the grouting port.

[0087] Step 3.2: Provide the model parameters that need to be calculated. To realize the unsteady-state effect of grout diffusion during the grouting process, a sinusoidal pulse pressure grouting method is defined at the grouting port. The analytical expression for the grouting pressure at the grouting port is as follows:

[0088] (8)

[0089] Among them, f z P1 and P2 represent the oscillation frequency, average pressure, and amplitude pressure of the sinusoidal pulse pressure, respectively; t up This indicates the grouting pressure rise time. Six working conditions were designed using three different rock fracture openings and two different grouting pressure pulse frequencies. The model parameters are summarized in Table 1, and the calculation working conditions are summarized in Table 2.

[0090] Table 1 Model parameters under all operating conditions

[0091]

[0092] Table 2 Calculation Condition Table

[0093]

[0094] Specifically, this embodiment of the invention also provides the specific content of step 4:

[0095] Step 4.1, as follows Figure 5 As shown, the computational domain is meshed, and spatial discretization is performed using polar coordinates:

[0096] The grid was generated using polar coordinates with a time step of 0.01 s and a spatial step of 0.01 m. Each grid cell corresponded to an independent control volume. The boundary of each control volume was defined by adjacent grid nodes and their connecting lines, and an staggered grid arrangement was used, i.e., the fracture aperture data b... i and slurry flow velocity data v i Stored at the control volume boundary (i.e., the grid node), slurry pressure P i Data is stored at the center of the control volume. With this setup, n grid space nodes and n-1 pressure space nodes can be formed, and the grid space nodes within the slurry diffusion front are defined as effective space nodes, and the pressure space nodes are defined as effective pressure space nodes.

[0097] In terms of time progression, a progressive time stepping strategy is adopted, while defining the superscript of physical quantities as the time step number and the subscript as the spatial step number. This method effectively captures the dynamic behavior and characteristics of fluids, accurately simulating complex physical processes while ensuring numerical stability.

[0098] Step 4.2: Discretize the slurry flow control equations and the unsteady slurry-rock coupled pressure control equations, and construct the discrete equations:

[0099] By combining the slurry flow control equation (1) and the unsteady slurry-rock coupled pressure control equation (3) in the simultaneous model, and spatially mapping the slurry reaction time, the pressure-velocity coupled control equation can be obtained:

[0100] (9)

[0101] in, The normal elastic modulus of the rock. Spatial mapping representing the degree of slurry reaction at different locations within the fracture.

[0102] Equation (9) can be used to solve for the slurry pressure within the slurry diffusion range. Based on the defined control volume and mesh, discretizing the left side of equation (9) yields:

[0103] (10)

[0104] Let the time of slurry reaction at all effective grid spatial nodes at time step j be denoted as . Discretizing the right side of equation (10) yields:

[0105] (11)

[0106] The crack aperture b, the viscosity u, and the yield stress τ0 all change with time along the slurry radiation diffusion direction. Combining equations (10) and (11), we can obtain the algebraic equation:

[0107] (12)

[0108] Define the number of effective grid nodes within the slurry diffusion front at the current time step j as: It can be used to store slurry flow rate and crack aperture data; after using an interlaced grid arrangement, it can obtain... -1 pressure space node, denoted as the effective pressure space node number. = -1, where the effective grid space nodes are... The quantitative solution will be described in detail in step 3. For each effective pressure space node i (i=1,2,..., All of them can satisfy the above algebraic equations. Therefore, the coefficient matrix can be extracted from equation (12). and the right-hand vector Among them, the assembly coefficient matrix Can be assembled into A zonal symmetric square matrix can be expressed as:

[0109] (13)

[0110] Elements in the assembly coefficient matrix and They can be represented as:

[0111] (14)

[0112] (15)

[0113] Right-hand vector The solution is obtained from the source term and the pressure from the previous time step. The composition, format, and elements of this vector can be expressed as follows:

[0114] (16)

[0115] (17)

[0116] (18)

[0117]

[0118] (19)

[0119] In the formula and These are the grouting pressure at the grouting port and the hydrostatic pressure at the grout diffusion front, respectively, where the grouting port pressure is... The parameters are known to vary with time, and the hydrostatic pressure is... Given the above, the discrete equations can be formed as follows:

[0120] (20)

[0121] Step 4.3: Discretize the grout volume conservation condition to obtain a real-time representation of the grout diffusion front radius; when calculating time step j after completing time step j-1, the data at the first pressure space node of time step j-1 needs to be used. The discrete form of equation (1) is calculated to obtain the slurry flow velocity at the injection port position at the current time step:

[0122] (twenty one)

[0123] The discrete equation for the total slurry flow rate at time step j is:

[0124] (twenty two)

[0125] The number of spatial nodes within the slurry diffusion front range at time step j. This is an unknown quantity. To calculate this value, we need to solve equation (22) by successive summation. Assuming that k successive summations will yield the amount of grout accumulated in the crack, the amount is:

[0126] (twenty three)

[0127] until Stop accumulating and take the number of valid grid space nodes. =k-1, and the effective number of pressure space nodes can be obtained simultaneously. Thus, the radius of the slurry diffusion front can be obtained:

[0128] (twenty four)

[0129] Step 4.4, as follows Figure 6 As shown, the spatial mapping of the slurry reaction time at grid nodes within the slurry range is captured.

[0130] It is known that a check valve is added at the grouting port to prevent grout backflow, meaning the grout flow rate at each time step is not less than 0, and the grout flow rate from the grouting port into the crack is recorded at each time step. ,set up Let be the radius of the grouting inlet, then the following condition is met:

[0131] (25)

[0132] Since the crack aperture varies in spatial distribution, equation (25) cannot be solved directly by integration. Instead, a successive accumulation method similar to that in equation (23) can be used to obtain the diffusion radius. Adjacent grid spatial nodes near the grouting port at the location :

[0133] (26)

[0134] The diffusion range of grout entering the fracture at different times was obtained. :

[0135] (27)

[0136] (28)

[0137] in, This represents the total amount of pulp produced from time step j-l+1 to time step j, and the effective grid nodes 1~ The difference in the total amount of slurry within the grid space nodes represents the value at each node. ~ The remaining grout within the +1 range. Further, starting from the grouting port, the grout range of each effective grid node can be captured sequentially, and the corresponding grout reaction time can be calculated using linear interpolation. (i=1,2,…, ):

[0138] (29)

[0139] Step 4.5: Iteratively correct the pressure and crack aperture distribution until the convergence condition is met, and finally output the grout pressure distribution, crack aperture change and grout diffusion range.

[0140] Since the fracture aperture distribution vector along the pressure path at time step j cannot be directly obtained, it is necessary to iteratively update the number of effective pressure space nodes and the pressure distribution vector by adjusting the fracture aperture distribution. Specifically, when entering the calculation at time step j, the fracture aperture distribution along the pressure path at the previous time step j-1 is first used as an example. As the initial iteration value, let it be denoted as The effective grid space nodes are calculated using equations (22) and (23). and the number of effective pressure space nodes The assembly matrix is ​​obtained based on the number of nodes in the effective pressure space. and the right-hand vector (Where the second superscript indicates the iteration number). The pressure distribution vector during the first iteration is then calculated using equation (20). :

[0141] (30)

[0142] Furthermore, a pressure distribution vector is used. The crack aperture in the next iteration is corrected using the Goodman model (2). Because an interleaved grid arrangement was used during the discretization process, the pressure data at the effective grid spatial nodes needs to be calculated based on the pressure data of their adjacent effective pressure spatial nodes when performing crack correction. Defining a linear relationship between the pressure distributions of adjacent effective spatial nodes, the grid nodes... The pressure at that point can be expressed as:

[0143] (31)

[0144] After recalculating the effective grid space nodes and effective pressure space nodes using the iterated fracture aperture distribution vector, the pressure friction distribution vector for the next iteration is calculated again using equation (30). Repeat the above steps until the error between two consecutive results in the nth iteration is reduced to an acceptable range, at which point the iteration stops. The final result is the pressure and fracture aperture distribution along the path at the current time step. Define the relative error of pressure and the equivalent error of fracture aperture distribution between two iterations as follows: and :

[0145] (32)

[0146] (33)

[0147] in, and Both are represented as the difference vector formed by the two iterations. -norm. When and When the convergence condition is met, the pressure and crack aperture distribution along the path, as well as the number of effective grid and pressure space nodes at the j-th time step, are output. The radius of the slurry diffusion front at the j-th time step is obtained by equation (24).

[0148] Step 4.6: When entering the next time step, repeat the steps 4.1 to 4.5 until the calculation termination time is reached. The program will then automatically stop the calculation and output the results.

[0149] Specifically, this embodiment of the invention also provides the specific content of step 5. Based on the calculation results of all the above steps, the slurry diffusion front radius curve and the slurry flow velocity curve at the injection port for each working condition can be obtained, such as... Figure 7 As shown, the distribution curves of grout pressure and crack aperture along the grouting path at a grouting time of 10 seconds are also presented. Figure 8 As shown.

[0150] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a simulation system for unsteady slurry diffusion processes considering slurry-rock coupling effects. This system is used to execute a simulation method for unsteady slurry diffusion processes considering slurry-rock coupling effects from the above method embodiments.

[0151] The system includes: a basic assumption setting module, used to define basic assumptions about slurry and fractures based on fracture flow theory; a governing equation establishment module, used to establish slurry flow control equations and fracture deformation control equations based on the basic assumptions about slurry and fractures; a coupling control equation establishment module, used to establish unsteady slurry-rock coupling pressure control equations based on the slurry flow control equations and fracture deformation control equations; a diffusion model establishment module, used to establish initial conditions, boundary conditions, and grouting body conditions based on the basic assumptions about slurry and fractures, and to build an unsteady slurry diffusion model considering the slurry-rock coupling effect by combining the unsteady slurry-rock coupling pressure control equations; and a model solution module, used to numerically solve the unsteady slurry diffusion model using the finite volume method, realizing the simulation of the unsteady slurry diffusion process considering the slurry-rock coupling effect.

[0152] The simulation system for unsteady slurry diffusion process considering slurry-rock coupling effect provided in this invention differs from existing models which are based on steady-state assumptions and neglect the unsteady effect of slurry pressure changing with time. This system employs several modules, based on fracture flow theory, and combines slurry flow, fracture deformation, and unsteady effects to construct a slurry diffusion model in fractured rock mass. The model is then numerically solved using the finite volume method (FVM), which can accurately simulate the slurry diffusion process in fractures, predict slurry pressure distribution, fracture aperture changes, and capture the slurry diffusion range at all times.

[0153] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides an electronic device, including a memory and a processor. The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize a simulation method for unsteady slurry diffusion process considering slurry-rock coupling effect as proposed in the above embodiments.

[0154] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, this program overcomes the problem of neglecting the unsteady-state effect of grout pressure changing with time in traditional models. It can efficiently and accurately simulate the diffusion process of grout in fractures, significantly improving computational efficiency. It is applicable to grouting design and optimization in fields such as tunnel engineering, mining engineering, and geological disaster prevention. It can provide theoretical support and technical guidance for engineering practice, optimize grouting parameters, improve grouting effect and engineering safety, reduce engineering costs, and significantly improve the scientificity and reliability of engineering design.

[0155] The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, or optical disk, used to store computer program code and necessary data files. The stored computer program includes: a basic assumption setting module, a control equation establishment module, a coupled control equation establishment module, a diffusion model establishment module, and a model solving module.

[0156] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A method for simulating unsteady slurry diffusion processes considering slurry-rock coupling effects, characterized in that, include: Based on fracture flow theory, the fundamental assumptions defining slurry and fractures include: (1) Assume that the slurry is an incompressible, homogeneous, and isotropic Bingham fluid; (2) Assume that the flow velocity of the grout on the upper and lower sidewalls of the crack is 0; (3) Assume that the grout only diffuses in the cracks; (4) Assume that the cracks are horizontally distributed; (5) Assume that the slurry flows in laminar flow within the fracture; (6) Assume that the rock mass on both sides of the fracture undergoes only elastic deformation; (7) Assume that the pressure at the slurry diffusion front is always equal to the static pressure; Based on fundamental assumptions about slurry and fractures, slurry flow control equations and fracture deformation control equations are established, including: The equation governing the flow of the slurry is expressed as follows: ， in, This represents the average flow of slurry diffusing along the fracture direction, where b represents the fracture aperture. Represents the time-varying function of slurry viscosity. This represents the real-variable function of the slurry yield stress. Indicates the slurry pressure gradient. This represents the critical pressure gradient at which Bingham fluid begins to flow; The expression for the crack deformation control equation is: ， Where b0 is the initial crack aperture, P is the grout pressure, and P s K is the threshold pressure for crack deformation. n K is the normal elastic coefficient, where K n =D / E, where D is the grouting influence range and E is the rock mass elastic modulus; Based on the slurry flow control equation and the fracture deformation control equation, an unsteady slurry-rock coupled pressure control equation is established, including: ， in, The distance between any point within the fissure and the grouting port. This represents the rate of change of grout pressure at any location within the fracture over time. The rate of change along the direction of slurry radiation diffusion. This represents the grout flow rate at any location within the fracture, where Indicates the crack aperture. Indicates the slurry flow rate; Based on the basic assumptions of grout and fractures, initial conditions, boundary conditions and grouting body conditions are established. Combined with the unsteady grout-rock coupling pressure control equation, an unsteady grout diffusion model considering the grout-rock coupling effect is built. The finite volume method is used to numerically solve the unsteady slurry diffusion model, realizing the simulation of the unsteady slurry diffusion process considering the slurry-rock coupling effect.

2. The method for simulating unsteady slurry diffusion processes considering slurry-rock coupling effects according to claim 1, characterized in that, Establish initial conditions, boundary conditions, and grouting volume conservation conditions, including: At the initial moment, the pressure at each location in the fracture is the fracture hydrostatic pressure. At the grouting port, the grouting pressure is set as a boundary condition, and at the grout diffusion front, the fracture hydrostatic pressure is set as a boundary condition. During the process of grout displacing the fracture medium, the volume of grout injected through the injection port and the volume of grout retained in the fracture are kept constant.

3. The method for simulating unsteady slurry diffusion processes considering slurry-rock coupling effects according to claim 1, characterized in that, The finite volume method is used to numerically solve the unsteady slurry diffusion model, including: The computational domain of the unsteady slurry diffusion model is meshed and spatially discretized using polar coordinates. The slurry flow control equation and the unsteady slurry-rock coupled pressure control equation are discretized, and discrete equations are constructed. Discretize the grout volume conservation condition to obtain a real-time characterization of the grout diffusion front radius; Spatial mapping and capture of the slurry reaction time at grid nodes within the slurry range; The pressure and crack aperture distributions are iteratively corrected until the convergence condition is met, and finally the slurry pressure distribution, crack aperture change and slurry diffusion range are obtained.

4. A simulation system for unsteady slurry diffusion processes considering slurry-rock coupling effects, used to implement the simulation method for unsteady slurry diffusion processes considering slurry-rock coupling effects as described in any one of claims 1-3, characterized in that, include: The basic assumption setting module is used to define the basic assumptions about slurry and fractures based on fracture flow theory; The governing equation establishment module is used to establish the slurry flow control equation and the crack deformation control equation based on the basic assumptions of slurry and cracks. The coupled control equation establishment module is used to establish unsteady magma-rock coupled pressure control equations based on slurry flow control equations and fracture deformation control equations. The diffusion model building module is used to establish initial conditions, boundary conditions and grouting body conditions based on the basic assumptions of grout and fractures. Combined with the unsteady grout-rock coupling pressure control equation, it builds an unsteady grout diffusion model that considers the grout-rock coupling effect. The model solver module is used to numerically solve the unsteady slurry diffusion model using the finite volume method, thereby simulating the unsteady slurry diffusion process that takes into account the slurry-rock coupling effect.

5. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the simulation method for unsteady slurry diffusion process considering the slurry-rock coupling effect as described in any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the simulation method for unsteady slurry diffusion process considering the slurry-rock coupling effect as described in any one of claims 1 to 3.

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